Equivalence of variance components between standard and recursive genetic models using LDL' transformations.

Area of Science:

• Quantitative genetics
• Animal breeding

Background:

• Recursive models propose causal relationships between traits.
• Statistical identification in recursive models requires parameter space restrictions.
• Likelihood equivalence exists between recursive and multiple trait models under certain conditions.

Purpose of the Study:

• To demonstrate the utility of LDL' or block-LDL' transformations for variance component estimation.
• To simplify inference in recursive models, especially with missing data.

Main Methods:

• Applied LDL' or block-LDL' transformations to variance component estimates from a multiple-trait mixed model.
• Utilized a Bayesian approach with a Gibbs sampler for variance component estimation.
• Tested the procedure on a large dataset of Pirenaica beef cattle traits.

Main Results:

• Variance components from a multiple-trait mixed model were successfully converted to estimates under recursive models.
• The transformations facilitated inference across multiple recursive models.
• The method proved effective even with large datasets and missing phenotypic records.

Conclusions:

• LDL' or block-LDL' transformations enable inference across multiple likelihood-equivalent recursive models.
• These transformations offer a method to handle missing data in recursive model analyses.
• The approach provides a flexible framework for genetic analyses using recursive models.